All-pass-filter-based single-phase phase-locked loop (APF-PLL) is a widely used grid synchronization method in grid-connected power converters. However, the performance of APF-PLL degrades under distorted grid conditions and the estimated phase and frequency will contain low-frequency oscillation terms, which is not conducive to practical application. To deal with this problem, this paper proposes two advanced APF-PLLs, which have good ability to suppress harmonics and dc offset interference without sacrificing the dynamic response of the system. In the first one, a band-pass filter (BPF) is used as the prefilter of APF-PLL to process the input voltage signal, and in the second one, the APF-PLL input signal is processed by using a harmonic decoupling network (HDN) and multiple prefilters. In addition, their parameter design procedure is also described in detail and is easy to follow. The experimental results presented in this paper finally verify the superiority and effectiveness of the two proposed methods.